In digital signal processing, there is a wide variety of filters for transforming a scanning rate. A scanning rates transformation refers to a conversion of an input sequence of a circuit, for example a filter, into an output sequence of the circuit, the input sequence and the output sequence having different signal rates or scanning rates.
With a finite impulse response (FIR) filter, very simple signal processing is effected at a high clock-pulse rate and complicated signal processing at a comparatively low clock-pulse rate. A FIR filter may be constructed in such a way that each input value is weighted with a filter coefficient and a sum of all weighted input values is subsequently formed. As weighting (i.e., multiplication by a coefficient) and addition frequently have to be carried out, the circuitry of digital signal processes is deliberately designed normally in such a way that the weighting and addition take place in one step or one command.
In FIR filters, a distinction is made between decimation filters and interpolation filters, which generally comprise an integrator stage and a further stage which operate at different clock frequencies. In a decimation filter, the input sequence has a higher signal rate than the output sequence whereas, in an interpolation filter, essentially the opposite occurs.
With a decimation filter having a decimation factor of 32 (i.e., ratio of the higher signal rate to the lower signal rate), 128 multiplications and additions are required at the low clock rate (e.g., during 128 taps), and this corresponds to four multiplications and additions at the high clock rate.
With FIR filters, almost randomly configured attenuation can be achieved in the pass and blocking band with respect to the transfer function of the FIR filters.
If a very narrow pass band is to be achieved with an FIR filter to be implemented with minimal expense, comb filters are frequently used (see “Multirate Filter Designs Using Comb Filters”, IEEE Transactions Circuit and Systems, pages 913-924, November 1984). During interpolation (a comb filter is used as the interpolation filter), the input sequence is applied to the further stage at a comparatively low signal rate and is converted into an output sequence with a high signal rate. During decimation, on the other hand (a comb filter is used as the decimation filter), the input sequence is applied to the integrator stage at a comparatively high signal rate and is converted into an output sequence with a comparatively low signal rate. In other words, the integrator stage of the comb filter operates at a higher clock frequency than its further stage, both as an interpolation filter and as a decimation filter. The integrator stage comprises at least one closed-loop controlled time-delay element or an integrator and the further stage comprises at least one time-delay element. A higher order comb filter is obtained if the integration stage comprises a plurality of closed-loop controlled delay elements or the further stage a plurality of time-delay elements. The structure of a comb filter is simple to construct in terms of circuitry.
However, in the comb filter the zero points of the transfer function are located on top of one another and not side by side, so the transfer function of the comb filter has narrow blocking bands, which explains the name “comb filter”.
Further, the closed-loop controlled time-delay elements or integrators of the integrator stage have an infinite memory, so a bit error which has occurred once, for example due to leakage, can only be corrected by disconnecting the comb filter.
For these and other reasons, there is a need for the present invention.